NEW YORK (Reuters) - U.S. crude prices settled about 3% lower on Tuesday after data showing domestic stockpiles didn’t rise as high as had been expected given tightening storage, despite pledges to cut production from May 1.

FILE PHOTO: An oil pump jack pumps oil in a field near Calgary, Alberta, Canada on July 21, 2014. REUTERS/Todd Korol

Markets were supported on hopes demand would recover after some authorities announced the easing of coronavirus-related restrictions. At least 16 U.S. states looked set to restart business, but Britain said it was too dangerous to relax the lockdown for fear of a second outbreak.

“Demand destruction has leveled off in the U.S., but production cuts have just begun in earnest,” said Phil Flynn, senior analyst at Price Futures Group.”

U.S. West Texas Intermediate (WTI) crude was down 44 cents, or 3.4%, at $12.34 a barrel. The contract plunged 25% on Monday.

Global benchmark Brent crude settled up 47 cents, or 2.3%, at $20.46 a barrel, following a 6.8% slide on Monday.

U.S. crude inventories rose by 10 million barrels in the week to April 24 to 510 million barrels, compared with analysts’ expectations for a build of 10.6 million barrels, data from industry group, the American Petroleum Institute, showed on Tuesday.

In the previous week, crude inventories rose by 15 million barrels to 518.6 million barrels, within striking distance of an all-time record of 535 million barrels set in 2017, the U.S. government said.

Globally, storage onshore was estimated to be about 85% full as of last week, according to data from consultancy Kpler.

In a sign of how desperate the industry is for places to store petroleum, oil traders are resorting to hiring expensive U.S. vessels to store gasoline or ship fuel overseas, shipping sources said.

Texas energy regulators will next week vote on a controversial proposal to reduce the state’s oil output after delaying it due to concerns about legal challenges.

As U.S. crude output continues to fall, shale producers are butting heads with their service companies over the termination of purchase agreements. Casillas Petroleum Resource Partners is suing Continental Resources for backing out of a $200 million oil and gas deal.

BP (BP.L) Chief Executive Bernard Looney told Reuters his company expected global oil demand to drop by about 15 million barrels per day (bpd) in the second quarter due to coronavirus-related movement restrictions.

That is more than the 10 million bpd of cuts agreed by the Organization of the Petroleum Exporting Countries, Russia and other allied producers. The reductions are due to be implemented from May 1.

OPEC oil supply in April is at its highest since December 2018, a company that tracks oil shipments said, as producers pump at will before the supply curbs takes effect.

Russian Energy Minister Alexander Novak said oil markets would start balancing out once an output deal took effect, but no significant rise in prices was likely in the near future due to high levels of global storage.

“Despite a frantic effort to reduce production, more output cuts will be required in the coming weeks before a price bottom

anywhere across the complex can be considered,” Jim Ritterbusch, president of Ritterbusch and Associates in Galena, Illinois, said in a report.